Statistics and Probability Commons^™

Examples Of Boundary Layers Associated With The Incompressible Navier-Stokes Equations, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated. All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions (specified velocity). These examples include a family of (nonlinear 3D) plane parallel flows, a family of (nonlinear) parallel pipe flows, as well as flows with uniform injection and suction at the boundary. We also identify a key ingredient in establishing the validity of the Prandtl type theory, i.e., a spectral constraint on the approximate solution to the Navier-Stokes system constructed by …

Virtual Manipulatives In The Classroom And Resulting Articles And Lesson Plans, Cheryl Juliana

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Upon coming across mathematical manipulatives generated and produced by Utah State University, as a math teacher, I conducted a classroom teaching experiment in three pre-algebra classes with students of various achievement levels. After teaching the entire year using no manipulatives in the classroom, I tested my students with a general, end-of-year, core criterion, or cumulative test. Their scores were noted. The students in the study group were then given opportunities to try several manipulatives offered on the "National Library of Virtual Manipulatives," both as a class, and alone, and then retested. The following paper gives the parameters of the study, …

A Comparative Study Between The Standards Of Learning And In-Class Grades., Randetta Lynn Fuller

Electronic Theses and Dissertations

We examined the Standards of Learning mathematics scores and in-class grades for a rural Virginia county public school system. We looked at third, fourth, fifth, sixth, and seventh grades as well as Algebra I, Algebra II, and Geometry classes. The purpose of this was to determine whether or not there is a strong correlation between the Standards of Learning and the students' in-class grades. Had a strong enough correlation between the Standards of Learning and in-class grades been found we would have used only the in-class grades to predict the Standard of Learning test scores. However, we found that the …

Spousal Concordance In Academic Achievements And Intelligence And Family-Based Association Studies Identified Novel Loci Associated With Intelligence., Yue Pan

Electronic Theses and Dissertations

Assortative Mating, the tendency for mate selection to occur on the basis of similar traits, plays an essential role in understanding the genetic variation on academic achievements and intelligence (IQ). It is an important mechanism explaining spousal concordance. We used principal component analysis (PCA) for spousal correlation. There is a significant positive correlation between spouses by the new variable PC1 (correlation coefficient=0.515, p<0.0001). We further research the genetic factor that affects IQ by using the same data. We performed a low density genome-wide association (GWA) analysis with a family-based association test to identify genetic variants that associated with intelligence as measured by WAIS full-score IQ (FSIQ). NTM at 11q25 (rs411280, p=0.000764) and NR3C2 at 4q31.23 (rs3846329, p=0.000675) were 2 novel genes that haven't been associated with IQ from other studies. This study may serve as a resource for replication in other populations and a foundation for future investigations.

Early Stopping Of A Neural Network Via The Receiver Operating Curve., Daoping Yu

Electronic Theses and Dissertations

This thesis presents the area under the ROC (Receiver Operating Characteristics) curve, or abbreviated AUC, as an alternate measure for evaluating the predictive performance of ANNs (Artificial Neural Networks) classifiers. Conventionally, neural networks are trained to have total error converge to zero which may give rise to over-fitting problems. To ensure that they do not over fit the training data and then fail to generalize well in new data, it appears effective to stop training as early as possible once getting AUC sufficiently large via integrating ROC/AUC analysis into the training process. In order to reduce learning costs involving the …

Thinking Outside The Curve, Part Ii: Modeling Fetal-Infant Mortality, Richard Charnigo, Lorie W. Chesnut, Tony Lobianco, Russell S. Kirby

Statistics Faculty Publications

BACKGROUND: Greater epidemiologic understanding of the relationships among fetal-infant mortality and its prognostic factors, including birthweight, could have vast public health implications. A key step toward that understanding is a realistic and tractable framework for analyzing birthweight distributions and fetal-infant mortality. The present paper is the second of a two-part series that introduces such a framework.

METHODS: We propose estimating birthweight-specific mortality within each component of a normal mixture model representing a birthweight distribution, the number of components having been determined from the data rather than fixed a priori.

RESULTS: We address a number of methodological issues related to our …

A Perturbation Method For Inference On Regularized Regression Estimates, Jessica Minnier, Lu Tian, Tianxi Cai

Harvard University Biostatistics Working Paper Series

No abstract provided.

Structural Measurements For Enhanced Mav Flight, John R. Singler, Gregg Abate, Benjamin T. Dickinson

Mathematics and Statistics Faculty Research & Creative Works

Our sense of touch allows us to feel the forces in our limbs when we walk, swim, or hold our arms out the window of a moving car. We anticipate this sense is key in the locomotion of natural flyers. Inspired by the sense of touch, the overall goal of this research is to develop techniques for the estimation of aerodynamic loads from structural measurements for flight control applications. We submit a general algorithm for the direct estimation of distributed steady loads over bodies from embedded noisy deformation-based measurements. The estimation algorithm is applied to a linearly elastic membrane test …

Asymptotic Analysis Of The Differences Between The Stokes-Darcy System With Different Interface Conditions And The Stokes-Brinkman System, Nan Chen, Max Gunzburger, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We consider the coupling of the Stokes and Darcy systems with different choices for the interface conditions. We show that, comparing results with those for the Stokes-Brinkman equations, the solutions of Stokes-Darcy equations with the Beavers-Joseph interface condition in the one-dimensional and quasi-two-dimensional (periodic) cases are more accurate than are those obtained using the Beavers-Joseph-Saffman-Jones interface condition and that both of these are more accurate than solutions obtained using a zero tangential velocity interface condition. the zero tangential velocity interface condition is in turn more accurate than the free-slip interface boundary condition. We also prove that the summation of the …

Roger Temam On The Occasion Of His 70th Birthday, Claude Michel Brauner, Danielle Hilhorst, Alain Miranville, Shouhong Wang, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

The Relationship Between The Level Of Support Group Participation And Psychosocial Factors In Prostate Cancer Patients Treated With Proton Therapy, Carol A. L. Davis

Loma Linda University Electronic Theses, Dissertations & Projects

Background. The role of support groups for cancer patients is known to be beneficial in helping people adjust to the disease, and cope with the myriad of effects that cancer has on quality of life. Although many people express interest in attending such support groups, few attend regularly. It is unclear what characteristics distinguish those who use such services from those who do not, especially among proton therapy patients.

Objective. To examine demographic and psychosocial characteristics associated with the Brotherhood of the Balloon (BOB) prostate cancer support group membership, a unique treatment-focused group originating at Loma Linda University Medical Center …

Estimating Teacher Effects Using Value-Added Models, Jennifer L. Green

Department of Statistics: Dissertations, Theses, and Student Research

Value-added modeling is an alternative approach to test-based accountability systems based on the proportions of students scoring at or above pre-determined proficiency levels. Value-added modeling techniques provide opportunities to estimate an individual teacher’s effect on student learning, while allowing for the possibility to control for the effect of non-educational factors beyond a school system’s control, such as socioeconomic status. However, numerous considerations exist when using value-added models to estimate teacher effects and defining what the teacher effects really describe. Chapter 2 provides an introduction to value-added methodology by describing several value-added models available for estimating teacher effects and their respective …

An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta

Applications and Applied Mathematics: An International Journal (AAM)

In this article Homotopy Perturbation Method (HPM) is applied to obtain an approximate analytical solution of a fractional diffusion equation with an external force and a reaction term different from the reaction term used by Das and Gupta (2010). The anomalous behavior of diffusivity in presence or absence of linear external force due to the presence of this force of reaction term are obtained and presented graphically.

Acm/Springer Mobile Networks And Applications (Monet) Special Issue On “Advanced Mobile Applications And Intelligent Multimedia Systems For Ubi-Com”, Jong Hyuk Park, Shu-Ching Chen, Mieso Denko, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

A Formal Context Specific Trust Model (Ftm) For Multimedia And Ubiquitous Computing Environment, Sheikh Iqbal Ahamed, Munirul M. Haque, Nilothpal Talukder

Mathematics, Statistics and Computer Science Faculty Research and Publications

In order to ensure secure sharing of resources in an ad-hoc network of handheld devices in a multimedia and ubiquitous computing environment, mutual collaboration is essential. However, the limitations, such as poor storage and computational capability of these multimedia and ubiquitous devices stand as the bottleneck for effective sharing of resources. As a result of this drawback, the adversaries are obtaining access to the new doors for security breaches. Mutual Trust is the weapon used to combat security violations by restricting malicious devices from participating in any interaction in such an open and dynamic environment. In this paper, we present …

Noise Assumptions In Complex-Valued Sense Mr Image Reconstruction, Daniel B. Rowe, Iain P. Bruce

Mathematics, Statistics and Computer Science Faculty Research and Publications

In fMRI, brain images are not measured instantaneously and a volume of images can take two seconds to acquire at a low 64x64 resolution. Significant effort has been put forth on many fronts to decrease image acquisition time including parallel imaging. In parallel imaging, sub-sampled spatial frequency points are measured in parallel and combined to form a single image. Measurement time is decreased at the expense of increased image reconstruction difficulty and time. One significant parallel imaging technique known as SENSE utilizes a complex-valued regression coefficient estimation process with transposes replaced by conjugate transposes. However, in SENSE the noise structure …

A Bayesian Approach To Dose-Response Assessment And Drug-Drug Interaction Analysis: Application To In Vitro Studies, Violeta G. Hennessey

Dissertations and Theses (Open Access)

The considerable search for synergistic agents in cancer research is motivated by the therapeutic benefits achieved by combining anti-cancer agents. Synergistic agents make it possible to reduce dosage while maintaining or enhancing a desired effect. Other favorable outcomes of synergistic agents include reduction in toxicity and minimizing or delaying drug resistance. Dose-response assessment and drug-drug interaction analysis play an important part in the drug discovery process, however analysis are often poorly done. This dissertation is an effort to notably improve dose-response assessment and drug-drug interaction analysis.

The most commonly used method in published analysis is the Median-Effect Principle/Combination Index method …

Arima Model For Forecasting Poisson Data: Application To Long-Term Earthquake Predictions, Wangdong Fu

UNLV Theses, Dissertations, Professional Papers, and Capstones

Earthquakes that occurred worldwide during the period of 1896 to 2009 with magnitude greater than or equal to 8.0 on the Richter scale are assumed to follow a Poisson process. Autoregressive Integrated Moving Average models are presented to fit the empirical recurrence rates, and to predict future large earthquakes. We show valuable modeling and computational techniques for the point processes and time series data. Specifically, for the proposed methodology, we address the following areas: data management and graphic presentation, model fitting and selection, model validation, model and data sensitivity analysis, and forecasting.

Thinking Outside The Curve, Part I: Modeling Birthweight Distribution, Richard Charnigo, Lorie W. Chesnut, Tony Lobianco, Russell S. Kirby

Statistics Faculty Publications

BACKGROUND: Greater epidemiologic understanding of the relationships among fetal-infant mortality and its prognostic factors, including birthweight, could have vast public health implications. A key step toward that understanding is a realistic and tractable framework for analyzing birthweight distributions and fetal-infant mortality. The present paper is the first of a two-part series that introduces such a framework.

METHODS: We propose describing a birthweight distribution via a normal mixture model in which the number of components is determined from the data using a model selection criterion rather than fixed a priori.

RESULTS: We address a number of methodological issues, including how the …

Principled Sure Independence Screening For Cox Models With Ultra-High-Dimensional Covariates, Sihai Dave Zhao, Yi Li

Harvard University Biostatistics Working Paper Series

No abstract provided.

A Unified Approach To Modeling Multivariate Binary Data Using Copulas Over Partitions, Bruce J. Swihart, Brian Caffo, Ciprian Crainiceanu

Johns Hopkins University, Dept. of Biostatistics Working Papers

Many seemingly disparate approaches for marginal modeling have been developed in recent years. We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the proposed copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalized models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate …

Fastmedusa: A Parallelized Tool To Infer Gene Regulatory Networks, Serdar Bozdag, Aiguo Li, Stefan Wuchty, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Motivation: In order to construct gene regulatory networks of higher organisms from gene expression and promoter sequence data efficiently, we developed FastMEDUSA. In this parallelized version of the regulatory network-modeling tool MEDUSA, expression and sequence data are shared among a user-defined number of processors on a single multi-core machine or cluster. Our results show that FastMEDUSA allows a more efficient utilization of computational resources. While the determination of a regulatory network of brain tumor in Homo sapiens takes 12 days with MEDUSA, FastMEDUSA obtained the same results in 6 h by utilizing 100 processors. Availability: Source code and documentation of …

The Role Of Rater Motivation In Personnel Selection Validation Studies, Dan Ispas

USF Tampa Graduate Theses and Dissertations

Personnel selection validation studies are routinely conducted in contemporary organizations for selecting and placing employees. Although numerous studies have been conducted with the goal of identifying new predictors, less research was focused on the criterion side. In the current paper, across three studies and five samples, I examined the role played by rater motivation in validation studies. I proposed that rater motivation would impact criterion-related validity of various predictors, the reliability, and the variance of performance ratings. In Study 1, these hypotheses were tested in two samples with varied operationalizations of predictors and of rater motivation. In Study 2, I …

Data Mining As Applied To The Socialsciences, Walter Morris

Cornerstone 3 Reports : Interdisciplinary Informatics

No abstract provided.

The Generation Of Domestic Electricity Load Profiles Through Markov Chain Modelling, Aidan Duffy, Fintan Mcloughlin, Michael Conlon

Conference Papers

Micro-generation technologies such as photovoltaics and micro-wind power are becoming increasing popular among homeowners, mainly a result of policy support mechanisms helping to improve cost competiveness as compared to traditional fossil fuel generation. National government strategies to reduce electricity demand generated from fossil fuels and to meet European Union 20/20 targets is driving this change. However, the real performance of these technologies in a domestic setting is not often known as high time resolution models for domestic electricity load profiles are not readily available. As a result, projections in terms of reducing electricity demand and financial paybacks for these micro-generation …

Probabilities In Probable Cause And Beyond: Statistical Versus Concrete Harms, Sherry F. Colb

Cornell Law Faculty Publications

No abstract provided.

Nonparametric Testing For Asymmetric Information, Liangjun Su, Martin Spindler

Research Collection School Of Economics

Asymmetric information is an important phenomenon in many markets and in particular in insurance markets. Testing for asymmetric information has become a very important issue in the literature in the last two decades. Almost all testing procedures that are used in empirical studies are parametric, which may yield misleading conclusions in the case of misspecification of either functional or distributional relationships among the variables of interest. Motivated by the literature on testing conditional independence, we propose a new nonparametric test for asymmetric information which is applicable in a variety of situations. We demonstrate the test works reasonably well through Monte …

Semi-Parametric Likelihood Functions For Bivariate Survival Data, S. H. Sathish Indika

Mathematics & Statistics Theses & Dissertations

Because of the numerous applications, characterization of multivariate survival distributions is still a growing area of research. The aim of this thesis is to investigate a joint probability distribution that can be derived for modeling nonnegative related random variables. We restrict the marginals to a specified lifetime distribution, while proposing a linear relationship between them with an unknown (error) random variable that we completely characterize. The distributions are all of positive supports, but one class has a positive probability of simultaneous occurrence. In that sense, we capture the absolutely continuous case, and the Marshall-Olkin type with a positive probability of …

A Study Of Relationships Between Family Members Using Familial Correlations, Corinne Wilson

Mathematics & Statistics Theses & Dissertations

Familial correlations measure the resemblance between family members and are used in many fields of study including epidemiology, genetics, heredity, and psychology. Here, an analysis of familial correlations where male and female children of the same family can have different correlations in the unequal family size case is presented. First, three likelihood based tests, namely the likelihood ratio test, Rao score test, and Wald test, and two more asymptotic tests which use Srivastava's estimator of the intraclass correlation coefficient are considered to test the null hypothesis of equality of the intraclass correlation coefficients when families have unequal numbers of children. …

Improving Statistical Analysis Of Prospective Clinical Trials In Stem Cell Transplantation. An Inventory Of New Approaches In Survival Analysis, Aurelien Latouche

COBRA Preprint Series

The CLINT project is an European Union funded project, run as a specific support action, under the sixth framework programme. It is a 2 year project aimed at supporting the European Group for Blood and Marrow Transplantation (EBMT) to develop its infrastructure for the conduct of trans-European clinical trials in accordance with the EU Clinical Trials Directive, and to facilitate International prospective clinical trials in stem cell transplantation. The initial task is to create an inventory of the existing biostatistical literature on new approaches to survival analyses that are not currently widely utilised. The estimation of survival endpoints is introduced, …